Substitution method 2 | Systems of equations | 8th grade | Khan Academy | Summary and Q&A

TL;DR

Substitution method is used to solve a system of equations by substituting one equation into another, but if the equations do not intersect, the system is inconsistent.

Key Insights

• 😑 The substitution method simplifies solving a system of equations by replacing one variable with an expression from another equation.
• 🫥 If the resulting equation is inconsistent, it means the lines represented by the equations do not intersect.
• 🟰 Inconsistent results are evident when illogical statements, like 16 equals -2, arise during the process.
• 🫥 Graphing the equations can visually confirm whether the lines intersect or are parallel.
• ❓ The substitution method is one of several approaches to solve systems of equations. Other methods include elimination and graphical methods.
• 😑 It is essential to correctly substitute the expression and simplify the resulting equation to avoid errors or inconsistent results.
• ❓ Systems of equations can have a unique solution (consistent), no solution (inconsistent), or infinitely many solutions.

Transcript

Use substitution to solve for x and y. And they give us a system of equations here. y is equal to negative 5x plus 8 and 10x plus 2y is equal to negative 2. So they've set it up for us pretty well. They already have y explicitly solved for up here. So they tell us, this first constraint tells us that y must be equal to negative 5x plus 8. So when w... Read More

Questions & Answers

Q: How does the substitution method work?

The substitution method involves solving one equation for a variable and substituting that expression into the other equation. This allows us to solve for the remaining variable. If both equations are linear and the resulting equation has a consistent solution, it gives the values for x and y that satisfy both equations.

Q: What does an inconsistent result mean?

An inconsistent result means that the system of equations does not have a common solution. In other words, the lines represented by the equations do not intersect on the coordinate plane. Inconsistent results are indicated by equations that lead to illogical statements, such as 16 equals -2.

Q: Are the lines represented by the equations in the video parallel?

Yes, the lines in the video are parallel. They have the same slope but different y-intercepts. When lines are parallel, they do not intersect and the system of equations has no solution.

Q: What is the significance of graphing the equations in addition to solving algebraically?

Graphing the equations visually represents the relationship between variables and provides a clear visualization of intersection points, if any. In this case, graphing the equations confirms that the lines are parallel and do not intersect, supporting the algebraic solution of an inconsistent system.

Summary & Key Takeaways

• The video explains the process of solving a system of equations using the substitution method.

• The first step is to isolate one variable in one of the equations.

• Then, substitute the expression for that variable into the other equation and solve for the remaining variable. If the resulting equation is inconsistent, it means the lines don't intersect and there is no solution.